A website on large numbers and fast-growing functions

Numbers from linear array notation

Here are some typical numbers from linear array notation. They’re also examples to help you understand LAN.

3-entry series

Those numbers are defined using s(a,b,c) with a, b, c > 1.

Tribo group

This group includes tribo, tetbo, pentbo and hexabo in order.

Tribo = s(3,3,2) = 3↑↑3 = 3^(3↑↑2) = 3^(3^(3↑↑1)) = 3^(3^3) = 3^27 = 7625597484987. It also equals those expressions: s(3,2,3) =(by rule 2) s(3,s(3,1,3),2) = s(3,s(3,1,2),2) = s(3,s(3,1,1),2) =(by rule 3) s(3,s(3,1),2) = s(3,3^1,2) = s(3,3,2). Using exAN, s(3,2{2}2) = s(3,2{1}1{1}2{2}1) = s(3,2,1,2) = s(3,3,2,1) = s(3,3,2). This numbers is quite small, even in real life. The amount of quarks in something weighing 32.2 grams, is about tribo squared. If we line tribo cubed quarks up, they just form a line about 47 thousand light years long, which is less than the radius of the milky way galaxy.